Why do you want to be White? You're an Arab, get over it, honor it, respect it.

I am not Arab, this question was merely asked out of curiosity. I am in no way or form advocating miscegnation/race-mixing. Ive actually learned something new , that nonwhite genes infact cannot be bred out but rather remain and same can be said for white genes. So judging by the answers here, an individual who has even a distant genetic al relation to a nonwhite is no longer a white person

If a mixed person from the mideastern background who has some white ancestry breeds with a white person will their children be white in appearance ? Or their grandchildren? Is it possible ?

Being white in appearence doesn't make them white. This is a difficult question and I don't know the answer but in my opinion, no. Most of us European Americans probably have some hair of non-white DNA that we don't and will never know about. Does it make us non-white? I don't think so. I hate to take the "sweep it under the rug" standpoint on this but, I defer to the "Who is white?" sticky. I think that's a pretty good policy concocted by far greater minds than my own.

It's simple... Take a cup of water and mix it with a cup of mud. Looks muddy right? Now keep adding just water over a period of time, and the mud "seemingly" disappears. The truth of the matter is that somewhere in that clear looking water is a speck of dirt. In the matter of genetic disposition, this covered gene could appear in some instance, however, the more you clarify the better it gets.

Human genetics have been mixed for thousands of years, and anyone who reads any truth in historical movement of peoples, will see that what you thought was a solid "culture" has actually been influenced at one time or another through mass migration or invasion. The thing that creates the appearance of solidity is nothing more than an overbearing need to stay within the confines of your own. So mix it on out. We are always searching for that mythical "100%."

Genetically, there is less than a few tenths of a percent difference between all humans. Thus, the basic genetic code that makes a human can be bred to any ethnicity at all.

In fact, all Middle Easterners north of Arabia were white. Im talking about Mesopotamia of course.
"Iran" literally means "Aryan." If you want to know the origin of the word "Aryan" it is actually derived from "Iranian."

Both mean exactly the same thing. Because in early times, "Iranians" were known for having a white complexion, blonde hair, and blue eyes.
In fact, they still live in Northern Pakistan and Iran--they never left. But much of Iran now contains people of Arabic descent (as in peoples who moved from Arabia).

Historically speaking, Iran and Indo-Europe is the origin of Caucasians. Which is why the word "Caucasians" is used: because the Caucus mountains are in this area of lower Russia.
They then moved north to Scandinavia and moved slightly south to Iran. This is historical proof that white genes can be bred out, as Iranians today aren't considered "Aryans" even though the very word "Aryan" comes from Iran. Thus, it proves that it's equally possible to breed nonwhite genes out. Though to be fair, blond-haired and blue-eyed natives still live in Iran and Pakistan and even areas of Afghanistan. For the most part, they keep to them selves in remote areas and are hardly bothered.
But they can be found to this day. The earliest establishment of whites on the globe is this, as it took several thousand more years to reach Western Europe.

I hope this answers your conundrum. This is the most detailed and thorough response I could muster.

If a mixed person from the mideastern background who has some white ancestry breeds with a white person will their children be white in appearance ? Or their grandchildren? Is it possible ?

White genes are not dominant. In theory, there is a chance that the children could look white. "In theory" you could even selectively breed a white person back out of the Obama line. In reality, the answer is probably NO. The odds of breeding out all the yucky genes are just too low.